B Discover the Reason Why Light Moves Slower in Water | Fermilab Video Explanation

[jeremyfiennes]

TL;DR Summary

Expanation via a secondary induced electric field is unsatisfactory

I watched a Fermilab video on light propagation in water: . He says (~) at time 7:50:
"The oscillating electric field of the light make electrons in the glass move. These set up a second oscillating electric field that combines with the first to make a single oscillating field. That is the wave that moves through matter. And it moves at a slower speed than light does in a vacuum".

He doesn't however explain the crucial point, namely why the combined wave moves slower. Since the second induced wave will have the same frequency as the original, there would seem to be no reason for it to do so.

 

[phyzguy]

The second induced wave does have the same frequency as the original. But it has a shorter wavelength. Since the speed is the wavelength times the frequency, the speed is slower.

 

[jeremyfiennes]

Thanks. In the video he shows them with the same wavelength. What then determines the wavelength?

 

[Ibix]

I don't recall doing light waves in media formally at the level of electromagnetism, so this is an educated guess. I expect you can derive a wave equation from Maxwell's equations in a medium, just as you can for in a vacuum. The speed is read off from the wave equation, and will obviously involve the properties of the medium that you fed in.

 

[jeremyfiennes]

I find this all a bit mysterious. Incoming light at frequency f excites electrons, that then presumably vibrate at f and (I would have thought) re-emit energy also at f, and hence the original wavelength c/f. The fact that he simply states the slower speed without explaining it I find suspicious. Could it be that the propagation of light in dense media is still not really understood?

 

[Ibix]

Could it be that the propagation of light in dense media is still not really understood?

No - I just don't know the exact details off the top of my head (although my guess would be that the derivation works the same way but with $D$ and $H$ instead of $E$ and $B$). Qualitatively, the point is that you can't treat the traveling electromagnetic wave and the fields of the nuclei and electrons of the medium separately, so it would be surprising if waves did travel at the same speed as they do in vacuum.

 

[jeremyfiennes]

Agreed. But it would be nice to be able to calculate that speed from the physical data of water.

 

[Nugatory]

it would be nice to be able to calculate that speed from the physical data of water.

We can and do. The permittivity and permeability are well-known physical properties of water; drop these into Maxwell’s equations and out comes the speed of light in water.

The difficulty we’re encountering in this thread comes from trying to use the microscopic atomic particle description of water when the behavior of light is determined by bulk properties of the medium.

 

[Cthugha]

Agreed. But it would be nice to be able to calculate that speed from the physical data of water.

That is doable, but tough. However, the fundamental physics of what is going on microscopically can be understood just from a very simplified model: the driven harmonic oscillator. Essentially the "second oscillating field" explanation just considers that there is a lot of physics going on within a material and all of this physics can be approximated in a very rough approximation in terms of a lot of harmonic oscillators driven (mostly) off-resonantly by the light field.

If you now have a look at what happens for driven harmonic oscillators (see e.g. figure 10 in these notes by Richard Fitzpatrick hosted by the university of Texas https://farside.ph.utexas.edu/teaching/315/Waves/node13.html ), you will notice the standard resonance behavior in the amplitudes shown on the left hand side of the figure. However, the important part is the right hand side - the phase response. You will find that the response is in phase with the driving field below resonance, but out of phase with it above the resonance frequency.
Intuitively, this makes sense. Any harmonic oscillator will just follow adiabatically if it is slowly displaced from its equilibrium position. However, if it is driven with very high frequency, inertia will become prominent and the response will be out of phase. This is a highly relevant effect here.
In a real material you now have huge numbers of resonances - intrinsic resonances, collective excitation modes of the material and many other things. For some of them, the light field may be below the resonance frequency. For many of them, the light field will be above the resonance frequency. All of these phase shifts add up and result in the observed "delay".

Of course reality is more complicated and considering individual isolated resonances is usually not a good model, but it is an okayish model to get a first intuition about what is going on.

 

[Lord Jestocost]

Summary:: Expanation via a secondary induced electric field is unsatisfactory

He doesn't however explain the crucial point, namely why the combined wave moves slower. Since the second induced wave will have the same frequency as the original, there would seem to be no reason for it to do so.

When light travels through a medium like water or glass, it appears to slow down. The apparent "slower speed" is the result of the superposition of two radiative electric fields: the incoming light, traveling at speed $c$, and the light re-radiated by the atoms in the medium (oscillating charges driven by the incoming light) in the forward direction, traveling at speed $c$, too.

The superposition shifts the phase of the radiation in the air downstream of the glass plate in the same way that would occur if the light were to go slower than $c$ in the glass plate.

To understand how the apparently slower velocity comes about, I recommend to read chapter 31 “The Origin of the Refractive Index” in “The Feynman Lectures on Physics, Volume I". On Bruce Sherwood’s homepage (https://brucesherwood.net/) you find an article “Refraction and the speed of light” dealing with this question, too.

 

[vanhees71]

Classical dispersion theory is indeed very intuitive and leads to the correct phenomenology although of course the true derivation should use quantum theory. It's nicely presented in the Feynman lectures:

https://www.feynmanlectures.caltech.edu/II_32.html

 

[tech99]

May I suggest that the wave slows down because it is coupled to a charge having inertia due to its connection to the molecule.